Mordell-Weil groups and the rank of elliptic curves over large fields

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Let K be a number field, (K) over bar an algebraic closure of K and E/K an elliptic curve defined over K. In this paper, we prove that if E/K has a K-rational point P such that 2P not equal O and 3P not equal O, then for each sigma is an element of Gal ((K) over bar /K), the Mordell-Weil group E((K) over bar (sigma)) of E over the fixed subfield of (K) over bar under sigma has infinite rank
Publisher
CANADIAN MATHEMATICAL SOC
Issue Date
2006-08
Language
English
Article Type
Article
Citation

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, v.58, no.4, pp.796 - 819

ISSN
0008-414X
DOI
10.4153/CJM-2006-032-4
URI
http://hdl.handle.net/10203/212951
Appears in Collection
MA-Journal Papers(저널논문)
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